Solution:Pearson's chi-squared test is used to assess three types of comparison: goodness of fit, homogeneity, and independence.
• A test of goodness of fit establishes whether an observed frequency distribution differs from a theoretical distribution.
• A test of homogeneity compares the distribution of counts for two or more groups using the same categorical variable (e.g. choice of activity-college, military, employment, travel-of graduates of a high school reported a year after graduation, sorted by graduation year, to see if number of graduates choosing a given activity has changed from class to class, or from decade to decade).
• A test of independence assesses whether observations consisting of measures on two variables, expressed in a contingency table, are independent of each other.